Roots of Polynomials

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How many solutions (roots) does the graph of a polynomial with no x-intercepts have?

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It has no solutions.

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What is the definition of a root of a polynomial?

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A root of a polynomial is a value of x that makes the polynomial equal to zero.

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What is the Fundamental Theorem of Algebra?

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The Fundamental Theorem of Algebra states that every non-constant polynomial has at least one complex root.

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What is the relationship between the degree of a polynomial and the number of roots it has?

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A polynomial of degree n has exactly n roots in the complex number system, counting multiplicities.

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What does it mean for a polynomial to have complex roots?

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Complex roots occur in conjugate pairs and are solutions to the polynomial that are not real numbers.

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What is a relative maximum in the context of polynomial graphs?

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A relative maximum is a point on the graph where the function value is higher than all nearby points.